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Can LLMs be used to discover new laws of logic?

Stephen Wolfram seems to claim this in What Is ChatGPT Doing … and Why Does It Work?, § "What Really Lets ChatGPT Work?":

is there a general way to tell if a sentence is meaningful? There’s no traditional overall theory for that. But it’s something that one can think of ChatGPT as having implicitly “developed a theory for” after being trained with billions of (presumably meaningful) sentences from the web, etc.

What might this theory be like? Well, there’s one tiny corner that’s basically been known for two millennia, and that’s logic. And certainly in the syllogistic form in which Aristotle discovered it, logic is basically a way of saying that sentences that follow certain patterns are reasonable, while others are not. Thus, for example, it’s reasonable to say “All X are Y. This is not Y, so it’s not an X” (as in “All fishes are blue. This is not blue, so it’s not a fish.”). And just as one can somewhat whimsically imagine that Aristotle discovered syllogistic logic by going (“machine-learning-style”) through lots of examples of rhetoric, so too one can imagine that in the training of ChatGPT it will have been able to “discover syllogistic logic” by looking at lots of text on the web, etc. (And, yes, while one can therefore expect ChatGPT to produce text that contains “correct inferences” based on things like syllogistic logic, it’s a quite different story when it comes to more sophisticated formal logic—and I think one can expect it to fail here for the same kind of reasons it fails in parenthesis matching.)

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    $\begingroup$ I'm not sure if he does claim this. It seems like he's saying that the logic discovered by ChatGPT depends on what it's train on, and any logic it discovers is already found in human text. $\endgroup$ Jul 24, 2023 at 5:10

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In the quoted text, Stephen Wolfram uses scare quotes to signify loose, non-technical analogies. So by my reading, he is not claiming that ChatGPT has discovered any new type of logic. Instead he is comparing ChatGPT's ability to output meaningful sentences loosely to classical logic.

The new "logic" that the model may have then, would be: Is this sentence meaningful? I.e. does it represent an idea that can be parsed and understood?

He then makes a comparison to existing classical logic (whether a statement is true or not), which ChatGPT does arguably approximate, and definitely parses and outputs simple logically correct statements better than chance.

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